An iron wire has a cross-sectional area equal to 1.45 10-5 m2. Carry out the fol

Question

An iron wire has a cross-sectional area equal to 1.45 10-5 m2. Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of 25.0 A. (a) How many kilograms are there in 1.00 mole of iron? kg/mol (b) Starting with the density of iron and the result of part (a), compute the molar density of iron (the number of moles of iron per cubic meter). mol/m3 (c) Calculate the number density of iron atoms using Avogadro's number. atoms/m3 (d) Obtain the number density of conduction electrons given that there are two conduction electrons per iron atom. electrons/m3 (e) Calculate the drift speed of conduction electrons in this wire.

Explanation / Answer

a)

M=55.85 g/mol =>0.05585 kg/mol

b)

density of iron p=7.86 Mg/m^3

Molar density =p/M=(7.86*10^3 kg/m^3)/0.05585 kg/mol

Molar density =1.41*10^5 mole/m^3

c)

n=(6.02*10^23 atoms/mol)(1.41*10^5 mole/m^3)

n=8.49*10^28 atoms/m^3

d)

=2*8.49*10^28 =1.7*10^29 electrons /m^3

e)

Vd =I/nqA =8/(1.7*10^29)(1.6*10^-19)(9.5*10^-6)

Vd=3.1*10^-5 m/s

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